Deep Thinking What Mathematics Can Teach Us About The Mind
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Deep Thinking
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Author : William Byers
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2015
Deep Thinking written by William Byers and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Education categories.
There is more than one way to think. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning. Deep thinking is a different and more basic way of using the mind. It results in the discontinuous "aha!" experience, which is the essence of creativity. It is at the heart of every paradigm shift or reframing of a problematic situation. The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. This book identifies the way in which the authentic intelligence of deep thinking differs from the artificial intelligence of "big data" and "analytics." Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Deep thinking can be found whenever one conceptual system morphs into another. The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. The approach is unusual and original. It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty.
Deep Thinking What Mathematics Can Teach Us About The Mind
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Author : William Byers
language : en
Publisher: World Scientific
Release Date : 2014-09-22
Deep Thinking What Mathematics Can Teach Us About The Mind written by William Byers and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-22 with Mathematics categories.
There is more than one way to think. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning. Deep thinking is a different and more basic way of using the mind. It results in the discontinuous “aha!” experience, which is the essence of creativity. It is at the heart of every paradigm shift or reframing of a problematic situation.The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. This book identifies the way in which the authentic intelligence of deep thinking differs from the artificial intelligence of “big data” and “analytics”.Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Deep thinking can be found whenever one conceptual system morphs into another.The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. The approach is unusual and original. It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty.
Ancient Greek I
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Author : Philip S. Peek
language : en
Publisher: Open Book Publishers
Release Date : 2021-10-19
Ancient Greek I written by Philip S. Peek and has been published by Open Book Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-19 with Literary Collections categories.
In this elementary textbook, Philip S. Peek draws on his twenty-five years of teaching experience to present the ancient Greek language in an imaginative and accessible way that promotes creativity, deep learning, and diversity. The course is built on three pillars: memory, analysis, and logic. Readers memorize the top 250 most frequently occurring ancient Greek words, the essential word endings, the eight parts of speech, and the grammatical concepts they will most frequently encounter when reading authentic ancient texts. Analysis and logic exercises enable the translation and parsing of genuine ancient Greek sentences, with compelling reading selections in English and in Greek offering starting points for contemplation, debate, and reflection. A series of embedded Learning Tips help teachers and students to think in practical and imaginative ways about how they learn. This combination of memory-based learning and concept- and skill-based learning gradually builds the confidence of the reader, teaching them how to learn by guiding them from a familiarity with the basics to proficiency in reading this beautiful language. Ancient Greek I: A 21st-Century Approach is written for high-school and university students, but is an instructive and rewarding text for anyone who wishes to learn ancient Greek.
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.
The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques
Thinking As Researchers Innovative Research Methodology Content And Methods
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Author : Nagwa Babiker Abdulla Yousif
language : en
Publisher: Xlibris Corporation
Release Date : 2023-02-12
Thinking As Researchers Innovative Research Methodology Content And Methods written by Nagwa Babiker Abdulla Yousif and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-12 with Reference categories.
This book is appropriate for undergraduate and graduate research methods courses as well as for instructors, academicians, social researchers, social workers and community development planners. The book aims to give a brief summary about the critical thinking and innovative research methods which are crucial in academic's promotion and knowledge building. Social Research Methods is one of the most important courses in the educational curriculum that adequately support students and researchers acquire the competencies they need to deal with complex data and new analytical tools. World is changing and accordingly, there are changing in the nature of data (for instance, big data, analytics etc.), and the complexity of the environment. University' instructors have to incorporate research in the undergraduate curriculum to allow the students to gain the knowledge and skills to learn the research process, not to conduct it per se, but, rather to use the research to bridge the gap between knowledge and critical decision-making.
The Best Writing On Mathematics 2015
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Author : Mircea Pitici
language : en
Publisher: Princeton University Press
Release Date : 2016-01-12
The Best Writing On Mathematics 2015 written by Mircea Pitici and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-12 with Mathematics categories.
The year's finest writing on mathematics from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it’s worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more. In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.
Humanizing Mathematics And Its Philosophy
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Author : Bharath Sriraman
language : en
Publisher: Birkhäuser
Release Date : 2017-11-07
Humanizing Mathematics And Its Philosophy written by Bharath Sriraman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.
This Festschrift contains numerous colorful and eclectic essays from well-known mathematicians, philosophers, logicians, and linguists celebrating the 90th birthday of Reuben Hersh. The essays offer, in part, attempts to answer the following questions set forth by Reuben himself as a focus for this volume: Can practicing mathematicians, as such, contribute anything to the philosophy of math? Can or should philosophers of math, as such, say anything to practicing mathematicians? Twenty or fifty years from now, what will be similar, and what will, or could, or should be altogether different: About the philosophy of math? About math education? About math research institutions? About data processing and scientific computing? The essays also offer glimpses into Reuben’s fertile mind and his lasting influence on the mathematical community, as well as revealing the diverse roots, obstacles and philosophical dispositions that characterize the working lives of mathematicians. With contributions from a veritable “who’s who” list of 20th century luminaries from mathematics and philosophy, as well as from Reuben himself, this volume will appeal to a wide variety of readers from curious undergraduates to prominent mathematicians.
From Giftedness To Gifted Education
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Author : Matthew C. Makel
language : en
Publisher: Routledge
Release Date : 2021-09-09
From Giftedness To Gifted Education written by Matthew C. Makel and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with Education categories.
The fields of gifted education and talent development have numerous theories and conceptions for how to identify and serve students. This book helps introduce and apply these ideas to help reflect theory in practice. Each chapter introduces readers to a different theory by providing definitions of key concepts, explaining the fundamental conceptual/theoretical approach, and concluding with advice on how the conception can be put into practice. Suggestions for further reading are also provided. Some chapters are based on theories that have been around for decades, and some have been developed more recently. But all chapters focus on helping empower readers to understand and take action without having to reinvent the wheel.
The Psychology Of Wisdom
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Author : Robert J. Sternberg
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
The Psychology Of Wisdom written by Robert J. Sternberg and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Psychology categories.
The Psychology of Wisdom: An Introduction is the first comprehensive coursebook on wisdom, providing an engaging, balanced, and expert introduction to the psychology of wisdom. It provides a comprehensive and up-to-date account of the psychological science of wisdom, covering wide-ranging perspectives. Each chapter includes extensive pedagogy, including a summary, a glossary, bolded terms, practical applications, discussion questions, and a brief description of the authors' research. Topics include the philosophical foundations, folk conceptions, and psychological theories of wisdom; relations of wisdom to morality and ethics, to personality and well-being, to emotion; wisdom and leadership, wisdom and social policy. These topics are covered in a non-technical, bias-free, and student-friendly manner. Written by the most eminent experts in the field, this is the definitive coursebook for undergraduate and graduate students, as well as interested professionals and researchers.
The Economics Of Transformation
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Author : Stefan Brunnhuber
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-06-02
The Economics Of Transformation written by Stefan Brunnhuber and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-02 with Business & Economics categories.
How can we transform our society? What is the role of finance in this process? The book will provide unconventional answers to these questions. Currently finance is still driving sustainability, but it should be the other way around: Sustainability should drive finance. Finance does not follow natural laws, but resembles conventions and reflects one of the most powerful leveragers to transform our society. This book provides multiple 'out of the box' solutions for the financial and monetary sector to shift our society towards a more sustainable future. Finance is the 'missing link' in the overall transformational process we are experiencing right now globally. Cases studies, descriptive tables and graphs and a variety of additional material on 'how the monetary system works' and 'how it should work' support the idea of a new and upcoming General Theory on financing our planetary commons, on money and a sustainable development for the 21st century and provides a compelling argument for the 'cheapest of all worlds'. This is the reader for scholars in the field, for politicians who have to make decisions, for bankers, investors and regulators who work in the financial sector and for everybody who has a bank account.